Experimenting Deep Convolutional Visual Feature Learning using Compositional Subspace Representation and Fashion-MNIST

This paper introduces a formal framework to model the convolutional visual feature learning in a convolutional neural network, which is called compositional subspace representation. The objective is to explain the convolutional visual feature learning computation using a rigid and structural method. The theoretical basis of the proposed framework is, the best way for representation to model a complex learning function is by using a composition of simple two-dimensional piecewise-linear functions to form a multilayers successive cascaded projection function for complex representation. Under the same hypothesis, the proposed framework also explains the hierarchical feature learning representation in a convolutional neural network, the well-acknowledged significant advantage of convolutional neural networks in visual computing. The proposed framework has experimented with image classification using the Fashion-MNIST dataset. Experimental assessments using learning curves analysis, confusion matrix, and visual assessment are presented and discussed. The experimental results were consistent with the theoretical expectation.